That's just crazy. You must have NHI, whether shakai hoken or kokumin kenko hoken. If you ever plan to stay here longer than that employer's contract and then switch to the latter, you will have to make backpayments for it.

Get either one now.

If the employer has you working more than 3/4 time (i.e., 3/4 x 40 = 30 hr/week or more), he is obligated by law to provide shakai hoken. If he weasels out of that like so many do (legally) by counting fewer hours for you (in the classroom only), then you get the other NHI.

Well, it kind of makes sense to me. I have health insurance at home under my parents plan. If anything serious happens, I would probably prefer to have it taken care of at home. So, I just need something to cover emergencies until I can get home to California.

Are you sure you risk losing your job if you join the national insurance system? If true, that's deeply shocking. Can you double check your facts?

The decision to join National Insurance is a no-brainer. If you stay here long term, sooner or later your status will change and you'll have to pay two years' backpayments (because, legally, you should have been on National Insurance all along). If you stay here short term, National Health Insurance is extremely cheap during your first year in Japan. (I was paying just 1100 Yen / month.) Without National Health Insurance, you risk the prospect of delays to emergency treatment while the hospital administrators try to figure out how to handle someone outside the system they're used to and wait for answers from your insurer. (I'm not scaremongering -- this does happen.) In the past, the Immigration Agency threatened to deny visa renewals to those who did not join -- this might come up again.

So, please please please join the National Health Insurance system. Sure, private insurance has its benefits, so you can get that as well if you want, but treat it as a top up to your National Insurance.

Join NHI. The premiums are deductible from your income and they're quite low your first year.

The serious things that will likely happen to a young adult are the kind where you don't have a choice where you're treated (such as being hit by a car). Private insurance probably won't cover much either if something like that happens.

Is your current insurance or future travel insurance actually accepted at most hospitals or clinics? You probably have to pay everything up front and then wait at least a month to get reimbursed.

Just how long do you have before you go to California? Accidents happen every day, you know. InFlames is right about first year of kokumin kenko hoken; it's about 2,500 yen/month because this is your first year here (it is, isn't it?), so there is no record of last year's Japanese earnings.